Question
(a) Define equivalent variation and compensating variation. Given an example of a problem for which equivalent variation would be an appropriate concept to apply. (b)
(a) Define equivalent variation and compensating variation. Given an example of a
problem for which equivalent variation would be an appropriate concept to apply.
(b) Find the Hicksian demand function for a consumer with u(x1, x2) = ?x1 + x2.
(c) The traditional celebration of Thanksgiving in the United States involves families
gathering together and eating a large meal that includes a whole roasted turkey. The
tradition is widely followed: over 95% of Thanksgiving meals include a turkey and twenty
times more turkeys are sold during the Thanksgiving week than in a normal week. An
initially puzzling observation is that supermarkets typically put turkeys on sale during this
week. Why might this occur?
2. (20 Minutes - 27 Points)
Suppose that Glenn Ellison is considering purchasing flood insurance for his house. If
Glenn does not buy flood insurance, his wealth will be w if there is no flood and w ? L if
there is a flood. The probability of a flood is ?.
The price of a policy that pays K if a flood occurs is cK. Assume that c
that the problem is otherwise uninteresting because Glenn would never buy any insurance.)
Assume that Glenn can choose any K ? [0,L], and that his choice of how much insurance
to buy maximizes his expected utility. Assume that Glenn's von Neumann Morgenstern
utility function u is a differentiable, strictly increasing and concave function of his final
wealth, i.e. Glenn maximizes (1 ? ?)u(w ? cK) + ?u(w ? L ? cK + K).
(a) Find the firstorder condition that characterizes Glenn's choice of K (assuming that
the parameters are such that an interior optimum exists.)
(b)For what value(s) of c will Glenn purchase full insurance? Does the answer depend
on the form of the utility function u? Why is this?
(c) Drop the assumptions that u is differentiable and concave - assume only that u is
strictly increasing and that a utilitymaximizing choice exists. Show that the K that Glenn
chooses is weakly increasing in the probability ? of a flood occurring.
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